Hyperbolas Topic 7.5

Definitions Hyperbola: set of all points where the absolute value of the difference of the distance from any point on the hyperbola to the foci is contant

Two Standard Equations Vertical Hyperbola: Foci: Vertices: Asymptote Slopes:

Two Standard Equations Horizontal Hyperbola: Foci: Vertices: Asymptote Slopes:

Writing in Standard Form Complete the square for both the x-terms and y-terms and move the constant to the other side of the equation The first term will be the positive term between x2 and y2 Divide all terms by the constant

Example: Group terms Complete the square Simplify Don’t forget to the negative nine! Divide by Constant

Graphing the hyperbola Put equation in standard form Graph the center (h, k) Graph the foci (look at the equation to determine your direction) Graph the vertices Graph the asymptotes (start at the center and use “Rise over Run”) Draw “U” shapes that go through the vertices and stay in between the asymptotes

Example: 1) Graph Center 2) Graph Foci 3) Graph Vertices 4) Graph Asymptotes 5) Graph Hyperbola

You Try! Write the following equation in standard form, then graph it.